In this chapter we summarise very briefly some general methods other than radial basis functions for the approximation and especially interpolation of multivariate data. The goal of this summary is to put the radial basis function approach into the context of other methods for approximation and interpolation, whereby the advantages and some potential disadvantages are revealed. It is particularly important to compare them with spline methods because in one dimension, for example, the radial basis function approach with integral powers (i.e. φ(r) = r or φ (r) = r3 for instance) simplifies to nothing else than a polynomial spline method. This is why we will concentrate on polynomial and polynomial spline methods. They are the most important ones and related to radial basis functions, and we will only touch upon a few others which are non(-piecewise-)polynomial. For instance, we shall almost completely exclude the so-called local methods although they are quite popular. They are local in the sense that there is not one continuous function s defined over the whole domain, where the data are situated, through the method for approximating all data. Instead, there is, for every x in the domain, an approximation s(x) sought which depends just on a few, nearby data. Thus, as x varies, this s(x) may not even be continuous in x (it is in some constructions). Typical cases are ‘natural neighbour’ methods or methods that are not interpolating but compute local least-squares approximations.